Problem: Rewrite as a simplified fraction. ${1.1\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 113.3333...\\ 10x &= 11.3333...\end{aligned}}$ Subtracting the two equations, we have: ${90x = 102}$ ${x = \dfrac{102}{90}} $ ${x = \dfrac{17}{15}} \text{or} {1 \dfrac{2}{15}}$